The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X  1  1 2X^2  1  1  X  X  1  X  1  1
 0  X  0  0 2X 2X^2+X  X 2X^2+2X 2X X^2 2X^2 2X^2+X 2X^2+X 2X^2+2X 2X 2X^2 X^2+X 2X^2+2X  X 2X^2+X  X 2X X^2 X^2+2X  0 2X^2+X 2X^2+2X  X  X 2X^2 2X^2 2X  X 2X^2+2X 2X X^2 2X^2+X X^2+X 2X^2+X  X 2X 2X^2+2X X^2 X^2 2X^2+2X 2X^2+X 2X^2+2X  0 2X^2+2X  0  0 2X 2X^2 2X  0  0 X^2 X^2 X^2+2X  0 2X X^2 2X^2+2X 2X X^2 2X^2+2X 2X^2+2X X^2+2X X^2 X^2+2X  X 2X^2 2X  0 X^2 2X^2+X 2X^2+2X  X X^2 X^2+X  0  0 2X 2X^2+X X^2+2X 2X X^2 X^2+2X  X 2X^2+2X X^2+X X^2 2X X^2 2X 2X^2+2X  0
 0  0  X 2X X^2 2X^2+2X  X 2X^2+X X^2+2X 2X^2+2X  0 2X^2+2X X^2 2X X^2  X  X X^2+X 2X  0 X^2+X 2X 2X^2+2X X^2+X X^2+X  0 2X^2 2X^2+2X  X  0 2X^2+2X X^2+X X^2 X^2  X X^2+X 2X 2X^2+X 2X X^2+X X^2+X 2X^2+2X  X X^2 2X^2+2X 2X^2 2X 2X 2X^2  0 X^2+2X  0 X^2+X  X 2X^2 X^2+X X^2 2X^2 X^2+2X X^2+2X 2X^2  X X^2 X^2+2X X^2+2X 2X^2+X X^2+X 2X^2+X 2X X^2 X^2+X  X 2X^2+2X X^2  0 X^2+2X X^2 X^2 X^2+2X  0 2X^2+X 2X^2+X X^2+X  X 2X^2  0  0 X^2+2X X^2+X 2X  0  X 2X^2+2X X^2 2X^2 2X^2+2X 2X^2+X
 0  0  0 X^2  0  0  0  0  0  0 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 2X^2  0 2X^2 X^2  0  0 2X^2 X^2 2X^2  0 X^2 2X^2 2X^2  0 X^2  0 X^2  0 X^2 X^2 2X^2 2X^2  0 X^2 X^2  0 X^2  0 2X^2  0  0 2X^2 X^2 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2  0  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2  0

generates a code of length 97 over Z3[X]/(X^3) who´s minimum homogenous weight is 186.

Homogenous weight enumerator: w(x)=1x^0+80x^186+252x^187+162x^188+278x^189+528x^190+324x^191+464x^192+1164x^193+546x^194+546x^195+1128x^196+342x^197+188x^198+150x^199+12x^200+44x^201+78x^202+30x^203+30x^204+48x^205+18x^206+16x^207+24x^208+24x^209+38x^210+18x^211+12x^213+12x^214+2x^222+2x^267

The gray image is a linear code over GF(3) with n=873, k=8 and d=558.
This code was found by Heurico 1.16 in 0.898 seconds.